In this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and Newton-Cotesmethods with positive coefficient for the solution of linear Fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. Here neural network isconsidered as a part of large field called neural computing orsoft computing. We propose alearning algorithm from the cost function for adjusting fuzzyweights. This paper is one of the first attempts to derive learningalgorithms from fuzzy neural networks with real input, fuzzy output,and fuzzy weights. Finally, we illustrate our approach by numerical examples.